Blow up and lifespan estimates for systems of semi-linear wave equations with dampings and potentials

TL;DR

This paper investigates the blow-up behavior and lifespan of solutions for semi-linear wave systems with space-dependent damping and potentials, providing critical blow-up regions and lifespan estimates.

Contribution

It introduces new blow-up regions and lifespan estimates for semi-linear wave systems with damping and potentials, extending previous results to more general settings.

Findings

Identified blow-up regions for three types of wave systems.

Derived lifespan estimates for solutions in these systems.

Extended understanding of wave system behavior with damping and potentials.

Abstract

In this paper, we consider the semi-linear wave systems with power-nonlinearities and space-dependent dampings and potentials. We obtain the blow-up regions for three types wave systems as well as the lifespan estimates.